• Structural Engineering and Mechanics
• /
• v.21 no.6
• /
• pp.635-658
• /
• 2005

The possibility of detecting a crack in L-shaped pipes filled with fluid based on measurement of transverse natural frequencies is examined. The problem is solved by representing the crack by a massless rotational spring, simulating the out-of-plane transverse vibration only without solving the coupled torsional vibration and using the transfer matrix method for solution of the governing equation. The theoretical solutions are verified by experiments. The cracks considered are external, circumferentially oriented and have straight front. Pipes made of aluminium and mild steel are tested with water as internal fluid. Crack size to pipe thickness ratio ranging from 0.20 to 0.57 and fluid (gauge) pressure in the range of 0 to 10 atmospheres are examined. The rotational spring stiffness is obtained by an inverse vibration analysis and deflection method. The details of the two methods are given. The results by the two methods are presented graphically and show good agreement. Crack locations are also determined by the inverse analysis. The maximum absolute error in the location is 13.80%. Experimentally determined variation of rotational spring stiffness with ratio of crack size to thickness is utilized to predict the crack sizes. The maximum absolute errors in prediction of crack size are 17.24% and 16.90% for aluminium and mild steel pipes respectively.

• Structural Engineering and Mechanics
• /
• v.42 no.3
• /
• pp.409-424
• /
• 2012

Since relatively low elasticity modulus of the FRP materials results in lower natural frequencies, it is necessary to study the free vibration of FRP transmission poles. In this paper, the free vibration of tapered FRP transmission poles with thin-walled circular cross-section is investigated by a tapered beam element. To model the flexible joints of the modular poles, a rotational spring model is used. Modal analysis is performed for typical FRP poles with/without joint and they are also modeled by ANSYS commercial finite element software. There is a good correlation between the results of the tapered beam finite element model and those obtained from ANSYS as well as the existing experimental results. The effects of different geometries, material lay-ups, concentrated masses at the pole tip, and joint flexibilities are evaluated. Moreover, it is concluded that using tougher fibres at the inner and outer layers of the cross-section, results in higher natural frequencies, significantly.

• Structural Engineering and Mechanics
• /
• v.85 no.4
• /
• pp.445-459
• /
• 2023

The current investigation is the first endeavor to apply the full layerwise finite element method (FEM) in free vibration analysis of functionally graded (FG) composite plates reinforced with graphene nanoplatelets (GPLs) in thermal environment. Unlike the equivalent single-layer (ESL) theories, the layerwise FEM focuses on all three-dimensional (3D) effects. The GPLs weight fraction is presumed invariable in each layer but varies through the plate thickness in a layerwise model. The modified Halpin-Tsai model is employed to acquire the effective Young's modulus. The rule of mixtures is applied to specify the effective Poisson's ratio and mass density. First, the current method is validated by comparing the numerical results with those stated in the available works. Next, a thorough numerical study is performed to examine the influence of various factors involving the pattern of distribution, weight fraction, geometry, and size of GPLs, together with the thickness-to-span ratio, thermal environment, and boundary conditions of the plate, on its free vibration behaviors. Numerical results demonstrate that employing a small percentage of GPL as reinforcement considerably grows the natural frequencies of the pure epoxy. Also, distributing more square-shaped GPLs, involving a smaller amount of graphene layers, and vicinity to the upper and lower surfaces make it the most efficient method to enhance the free vibration behaviors of the plate.

• Structural Engineering and Mechanics
• /
• v.24 no.5
• /
• pp.543-560
• /
• 2006

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.14 no.11
• /
• pp.1066-1074
• /
• 2004

A vibration isolation system for a large reverberation chamber (1,228 $m^3$ and 1,000 ton) has been installed and verified. The reverberation chamber generates loud noise and induces high level of vibration while performing spacecraft acoustic reliability tests. The isolation system prevents vibration transfer from the chamber to the enclosure buildings. This paper describes design process and commissioning experiments of the system. Design criteria have been derived from rigid body model of the chamber. The stiffness of neoprene pads has been selected by employing finite element analysis of the reverberant chamber and isolation system. A total of 21 neoprene pads have been installed between the chamber and supporting Pedestals. A sand bag of 800kg was dropped on the chamber floor to measure the natural frequency of the isolation system. While 136.9 dB noise is generated in the chamber, absolute transmissibility of the isolation system has been measured. The measured natural frequency of the chamber is 10.2Hz, which is 80% of the predicted value. Overall transmissibility at working frequency range (25∼10.000 Hz) is less than -12.4 dB.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.12 no.5
• /
• pp.330-337
• /
• 2002

A frequency equation of beam subjected to the axial load and having ηthrough-the-width-splits is developed. The beam comprises of beam elements that are split into the upper and the lower part, and non-split beam elements. Equations of motion of each beam element are non-dimensionalized with respect to length. The frequency equation of beam is derived from that of each beam element, which satisfies the displacement of the longitudinal and transverse vibration and the boundary conditions between the beam elements. Numerical simulation and experimental work for the beam having several split beam elements are carried out to demonstrate the analytical development and its validity. The experimental results are in good agreement with those of the present frequency equation. The relationships between the split beam width and natural frequencies, and also the relationships between number of split and natural frequencies, in case that the total beam split length is same. are discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2014.10a
• /
• pp.36-41
• /
• 2014

Electro-Mechanical Actuator installed on aircraft consists of a decelerator which magnifies the torque to rotate an axis connected with aircraft control surface, a control section which controls the motor assembly through receiving orders from cockpit and a motor assembly which rotates the decelerator. EMA controls aircraft attitued, position, landing, takeoff, etc. It is important part of a aircraft. Aircraft maneuvering make vibration of EMA. Vibration may cause the vibration fatigue. For that reason, it is necessary to analyze the system safety. In this paper, first EMA is modeled in finite element method and analyzed the response from input vibration. second EMA is tested and analyzed from modal experimental data. third EMA Fe model is updated and re analyzed. and EMA is verified safety with $3{\sigma}$ stress and S/N curves.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2004.11a
• /
• pp.526-529
• /
• 2004

Arches are one of the most important basic structural units as well as the beams, columns and plates. Most complicated structures consist of only these basic units and therefore it is very attractive research subject to analysis both the static and dynamic behavior of such units including the arches. This study deals with the free vibration of arbitrary shaped arches. In order to obtain the exactly arch shape, which surveyed (x, y) of neutral axis of arbitrary shaped arches are compared to various shape of arch: circular, parabolic, sinusoidal, elliptic, spiral and cartenary. The differential equations governing free vibrations of arches are merely adopted in the open literature rather than deriving the equations in this study. The Taylor series method is used as the numerical differential scheme. The Runge-Kutta method and the Regula-Falsi method, respectively, are used to integrate the governing differential equations and to compute the natural frequencies It is expected that results obtained herein can be practically utilized in the fields of vibration control.

• Advances in nano research
• /
• v.14 no.6
• /
• pp.521-525
• /
• 2023

This paper concerned with the vibration of double walled carbon nanotubes (CNTs) as continuum model based on Timoshenko-beam theory. The vibration solution obtained from Timoshenko-beam theory provides a better presentation of vibration structure of carbon nanotubes. The natural frequencies of double-walled CNTs against half axial wave mode are investigated. The frequency decreases on decreasing the half axial wave mode. The shape of frequency arcs is different for various lengths. It is observed that model has produced lowest results for C-F and highest for C-C. A large parametric study is performed to see the effect of half axial wave mode on frequencies of CNTs. This numerically vibration solution delivers a benchmark results for other techniques. The comparison of present model is exhibited with previous studies and good agreement is found.

• Smart Structures and Systems
• /
• v.16 no.6
• /
• pp.1023-1047
• /
• 2015

In this study, the optimal location of the MR fluid segments in a partially treated laminated composite sandwich plate has been identified to maximize the natural frequencies and the loss factors. The finite element formulation is used to derive the governing differential equations of motion for a partially treated laminated composite sandwich plate embedded with MR fluid and rubber material as the core layer and laminated composite plate as the face layers. An optimization problem is formulated and solved by combining finite element analysis (FEA) and genetic algorithm (GA) to obtain the optimal locations to yield maximum natural frequency and loss factor corresponding to first five modes of flexural vibration of the sandwich plate with various combinations of weighting factors under various boundary conditions. The proposed methodology is validated by comparing the natural frequencies evaluated at optimal locations of MR fluid pockets identified through GA coupled with FEA and the experimental measurements. The converged results suggest that the optimal location of MR fluid pockets is strongly influenced not only by the boundary conditions and modes of vibrations but also by the objectives of maximization of natural frequency and loss factors either individually or combined. The optimal layout could be useful to apply the MR fluid pockets at critical components of large structure to realize more efficient and compact vibration control mechanism with variable damping.